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Background School environments are thought to play an important role in the community spread of infectious diseases such as influenza because of the high mixing rates of school children. The closure of schools has therefore been proposed as an efficient mitigation strategy. Such measures come however with high associated social and economic costs, making alternative, less disruptive interventions highly desirable. The recent availability of high-resolution contact network data from school environments provides an opportunity to design models of micro-interventions and compare the outcomes of alternative mitigation measures. Methods and results We model mitigation measures that involve the targeted closure of school classes or grades based on readily available information such as the number of symptomatic infectious children in a class. We focus on the specific case of a primary school for which we have high-resolution data on the close-range interactions of children and teachers. We simulate the spread of an influenza-like illness in this population by using an SEIR model with asymptomatics, and compare the outcomes of different mitigation strategies. We find that targeted class closure affords strong mitigation effects: closing a class for a fixed period of time – equal to the sum of the average infectious and latent durations – whenever two infectious individuals are detected in that class decreases the attack rate by almost 70% and significantly decreases the probability of a severe outbreak. The closure of all classes of the same grade mitigates the spread almost as much as closing the whole school. Conclusions Our model of targeted class closure strategies based on readily available information on symptomatic subjects and on limited information on mixing patterns, such as the grade structure of the school, shows that these strategies might be almost as effective as whole-school closure, at a much lower cost. This may inform public health policies for the management and mitigation of influenza-like outbreaks in the community.

The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.

Italy has been severely affected by the COVID-19 pandemic, reporting the highest death toll in Europe as of April 2020. Following the identification of the first infections, on February 21, 2020, national authorities have put in place an increasing number of restrictions aimed at containing the outbreak and delaying the epidemic peak. On March 12, the government imposed a national lockdown. To aid the evaluation of the impact of interventions, we present daily time-series of three different aggregated mobility metrics: the origin-destination movements between Italian provinces, the radius of gyration, and the average degree of a spatial proximity network. All metrics were computed by processing a large-scale dataset of anonymously shared positions of about 170,000 de-identified smartphone users before and during the outbreak, at the sub-national scale. This dataset can help to monitor the impact of the lockdown on the epidemic trajectory and inform future public health decision making.Measurement(s)mobilityTechnology Type(s)GPS navigation systemFactor Type(s)temporal intervalSample Characteristic - OrganismHomo sapiensSample Characteristic - LocationItalyMachine-accessible metadata file describing the reported data: 10.6084/m9.figshare.12515256

Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at different time points. However, quantifying the similarity between temporal graphs as a whole is an open problem. Here, we use embeddings based on time-respecting random walks to introduce a new notion of distance between temporal graphs. This distance is well-defined for pairs of temporal graphs with different numbers of nodes and different time spans. We study the case of a matched pair of graphs, when a known relation exists between their nodes, and the case of unmatched graphs, when such a relation is unavailable and the graphs may be of different sizes. We use empirical and synthetic temporal network data to show that the distance we introduce discriminates graphs with different topological and temporal properties. We provide an efficient implementation of the distance computation suitable for large-scale temporal graphs. Temporal graphs can be applied to represent time-evolving complex natural systems, describing the evolution of the interactions between system elements, however quantifying the similarity between temporal graphs remains an open problem. The authors introduce a notion of distance to compare time-resolved interaction patterns, based on their representations as temporal graphs.

Mobile phone data have been extensively used to study urban mobility. However, studies based on gender-disaggregated large-scale data are still lacking, limiting our understanding of gendered aspects of urban mobility and our ability to design policies for gender equality. Here we study urban mobility from a gendered perspective, combining commercial and open datasets for the city of Santiago, Chile. We analyze call detail records for a large cohort of anonymized mobile phone users and reveal a gender gap in mobility: women visit fewer unique locations than men, and distribute their time less equally among such locations. Mapping this mobility gap over administrative divisions, we observe that a wider gap is associated with lower income and lack of public and private transportation options. Our results uncover a complex interplay between gendered mobility patterns, socio-economic factors and urban affordances, calling for further research and providing insights for policymakers and urban planners.

Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To assess the relevance of such structures, we explore the effectiveness of strategies aimed either at containing or maximizing the impact of a spread, based respectively on removing span-cores of high cohesiveness or duration to decrease the epidemic risk, or on seeding the process from such structures. The effectiveness of such strategies is assessed in a variety of empirical data sets and compared to baselines that use only static information on the centrality of nodes and static concepts of coreness, as well as to a baseline based on a temporal centrality measure. Our results show that the most stable and cohesive temporal cores play indeed an important role in epidemic processes on temporal networks, and that their nodes are likely to include influential spreaders.

Digital networks, mobile devices, and the possibility of mining the ever-increasing amount of digital traces that we leave behind in our daily activities are changing the way we can approach the study of human and social interactions. Large-scale datasets, however, are mostly available for collective and statistical behaviors, at coarse granularities, while high-resolution data on person-to-person interactions are generally limited to relatively small groups of individuals. Here we present a scalable experimental framework for gathering real-time data resolving face-to-face social interactions with tunable spatial and temporal granularities. We use active Radio Frequency Identification (RFID) devices that assess mutual proximity in a distributed fashion by exchanging low-power radio packets. We analyze the dynamics of person-to-person interaction networks obtained in three high-resolution experiments carried out at different orders of magnitude in community size. The data sets exhibit common statistical properties and lack of a characteristic time scale from 20 seconds to several hours. The association between the number of connections and their duration shows an interesting super-linear behavior, which indicates the possibility of defining super-connectors both in the number and intensity of connections. Taking advantage of scalability and resolution, this experimental framework allows the monitoring of social interactions, uncovering similarities in the way individuals interact in different contexts, and identifying patterns of super-connector behavior in the community. These results could impact our understanding of all phenomena driven by face-to-face interactions, such as the spreading of transmissible infectious diseases and information.

Contacts between patients, patients and health care workers (HCWs) and among HCWs represent one of the important routes of transmission of hospital-acquired infections (HAI). A detailed description and quantification of contacts in hospitals provides key information for HAIs epidemiology and for the design and validation of control measures. We used wearable sensors to detect close-range interactions (\"contacts\") between individuals in the geriatric unit of a university hospital. Contact events were measured with a spatial resolution of about 1.5 meters and a temporal resolution of 20 seconds. The study included 46 HCWs and 29 patients and lasted for 4 days and 4 nights. 14,037 contacts were recorded overall, 94.1% of which during daytime. The number and duration of contacts varied between mornings, afternoons and nights, and contact matrices describing the mixing patterns between HCW and patients were built for each time period. Contact patterns were qualitatively similar from one day to the next. 38% of the contacts occurred between pairs of HCWs and 6 HCWs accounted for 42% of all the contacts including at least one patient, suggesting a population of individuals who could potentially act as super-spreaders. Wearable sensors represent a novel tool for the measurement of contact patterns in hospitals. The collected data can provide information on important aspects that impact the spreading patterns of infectious diseases, such as the strong heterogeneity of contact numbers and durations across individuals, the variability in the number of contacts during a day, and the fraction of repeated contacts across days. This variability is however associated with a marked statistical stability of contact and mixing patterns across days. Our results highlight the need for such measurement efforts in order to correctly inform mathematical models of HAIs and use them to inform the design and evaluation of prevention strategies.

Little quantitative information is available on the mixing patterns of children in school environments. Describing and understanding contacts between children at school would help quantify the transmission opportunities of respiratory infections and identify situations within schools where the risk of transmission is higher. We report on measurements carried out in a French school (6-12 years children), where we collected data on the time-resolved face-to-face proximity of children and teachers using a proximity-sensing infrastructure based on radio frequency identification devices. Data on face-to-face interactions were collected on Thursday, October 1(st) and Friday, October 2(nd) 2009. We recorded 77,602 contact events between 242 individuals (232 children and 10 teachers). In this setting, each child has on average 323 contacts per day with 47 other children, leading to an average daily interaction time of 176 minutes. Most contacts are brief, but long contacts are also observed. Contacts occur mostly within each class, and each child spends on average three times more time in contact with classmates than with children of other classes. We describe the temporal evolution of the contact network and the trajectories followed by the children in the school, which constrain the contact patterns. We determine an exposure matrix aimed at informing mathematical models. This matrix exhibits a class and age structure which is very different from the homogeneous mixing hypothesis. We report on important properties of the contact patterns between school children that are relevant for modeling the propagation of diseases and for evaluating control measures. We discuss public health implications related to the management of schools in case of epidemics and pandemics. Our results can help define a prioritization of control measures based on preventive measures, case isolation, classes and school closures, that could reduce the disruption to education during epidemics.